Basic theorems about obs-sdom-info-list-p, generated by deflist.
Theorem:
(defthm obs-sdom-info-list-p-of-cons (equal (obs-sdom-info-list-p (cons acl2::a x)) (and (obs-sdom-info-p acl2::a) (obs-sdom-info-list-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-cdr-when-obs-sdom-info-list-p (implies (obs-sdom-info-list-p (double-rewrite x)) (obs-sdom-info-list-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-when-not-consp (implies (not (consp x)) (equal (obs-sdom-info-list-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-p-of-car-when-obs-sdom-info-list-p (implies (obs-sdom-info-list-p x) (iff (obs-sdom-info-p (car x)) (or (consp x) (obs-sdom-info-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-obs-sdom-info-list-p-compound-recognizer (implies (obs-sdom-info-list-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm obs-sdom-info-list-p-of-list-fix (implies (obs-sdom-info-list-p x) (obs-sdom-info-list-p (acl2::list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-append (equal (obs-sdom-info-list-p (append acl2::a acl2::b)) (and (obs-sdom-info-list-p (acl2::list-fix acl2::a)) (obs-sdom-info-list-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-rev (equal (obs-sdom-info-list-p (acl2::rev x)) (obs-sdom-info-list-p (acl2::list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-butlast (implies (obs-sdom-info-list-p (double-rewrite x)) (obs-sdom-info-list-p (butlast x acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-sfix (iff (obs-sdom-info-list-p (set::sfix x)) (or (obs-sdom-info-list-p x) (not (set::setp x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-insert (iff (obs-sdom-info-list-p (set::insert acl2::a x)) (and (obs-sdom-info-list-p (set::sfix x)) (obs-sdom-info-p acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-delete (implies (obs-sdom-info-list-p x) (obs-sdom-info-list-p (set::delete acl2::k x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-mergesort (iff (obs-sdom-info-list-p (set::mergesort x)) (obs-sdom-info-list-p (acl2::list-fix x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-union (iff (obs-sdom-info-list-p (set::union x acl2::y)) (and (obs-sdom-info-list-p (set::sfix x)) (obs-sdom-info-list-p (set::sfix acl2::y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-intersect-1 (implies (obs-sdom-info-list-p x) (obs-sdom-info-list-p (set::intersect x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-intersect-2 (implies (obs-sdom-info-list-p acl2::y) (obs-sdom-info-list-p (set::intersect x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-difference (implies (obs-sdom-info-list-p x) (obs-sdom-info-list-p (set::difference x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-rcons (iff (obs-sdom-info-list-p (acl2::rcons acl2::a x)) (and (obs-sdom-info-p acl2::a) (obs-sdom-info-list-p (acl2::list-fix x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-p-when-member-equal-of-obs-sdom-info-list-p (and (implies (and (member-equal acl2::a x) (obs-sdom-info-list-p x)) (obs-sdom-info-p acl2::a)) (implies (and (obs-sdom-info-list-p x) (member-equal acl2::a x)) (obs-sdom-info-p acl2::a))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-when-subsetp-equal (and (implies (and (subsetp-equal x acl2::y) (obs-sdom-info-list-p acl2::y)) (equal (obs-sdom-info-list-p x) (true-listp x))) (implies (and (obs-sdom-info-list-p acl2::y) (subsetp-equal x acl2::y)) (equal (obs-sdom-info-list-p x) (true-listp x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-set-difference-equal (implies (obs-sdom-info-list-p x) (obs-sdom-info-list-p (set-difference-equal x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-intersection-equal-1 (implies (obs-sdom-info-list-p (double-rewrite x)) (obs-sdom-info-list-p (intersection-equal x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-intersection-equal-2 (implies (obs-sdom-info-list-p (double-rewrite acl2::y)) (obs-sdom-info-list-p (intersection-equal x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-union-equal (equal (obs-sdom-info-list-p (union-equal x acl2::y)) (and (obs-sdom-info-list-p (acl2::list-fix x)) (obs-sdom-info-list-p (double-rewrite acl2::y)))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-p-of-nth-when-obs-sdom-info-list-p (implies (and (obs-sdom-info-list-p x) (< (nfix acl2::n) (len x))) (obs-sdom-info-p (nth acl2::n x))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-take (implies (obs-sdom-info-list-p (double-rewrite x)) (iff (obs-sdom-info-list-p (take acl2::n x)) (or (obs-sdom-info-p nil) (<= (nfix acl2::n) (len x))))) :rule-classes ((:rewrite)))
Theorem:
(defthm obs-sdom-info-list-p-of-repeat (iff (obs-sdom-info-list-p (acl2::repeat acl2::n x)) (or (obs-sdom-info-p x) (zp acl2::n))) :rule-classes ((:rewrite)))